Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 463-473

REMOVABILITY AND NON-INJECTIVITY OF CONFORMAL WELDING

Malik Younsi

University of Hawaii at Manoa, Department of Mathematics
Honolulu, HI 96822, U.S.A.; malik.younsi 'at' gmail.com

Abstract. We construct a (non-removable) Jordan curve Γ and a non-Möbius homeomorphism of the Riemann sphere which is conformal on the complement of Γ and maps the curve Γ onto itself. The curve is flexible in the sense of Bishop and may be taken to have zero area. The existence of such curves and conformal homeomorphisms is closely related to the non-injectivity of conformal welding.

2010 Mathematics Subject Classification: Primary 30C35; Secondary 37E10, 30C85.

Key words: Conformal welding, removability, flexible curves, capacity.

Reference to this article: M. Younsi: Removability and non-injectivity of conformal welding. Ann. Acad. Sci. Fenn. Math. 43 (2018), 463-473.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4322